Implement 1D convex minimization in Python

Q: Implement 1D convex minimization in Python

This is a Machine Learning interview question from Uber for Machine Learning Engineer roles. View the full question and solution on PracHub.

Q: How do I approach Machine Learning interview questions?

Machine Learning questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master machine learning interviews.

Question

1D Black-Box Convex Minimization (Gradient-Free)

Task

Implement in Python an algorithm to minimize a 1D convex function F(x) over a closed interval [a, b] when gradients are unavailable and only function evaluations are allowed.

Requirements

Describe the approach (e.g., golden-section search) and why it works for 1D convex functions.
Specify stopping criteria and numerical tolerances.
Analyze the number of function evaluations and time/space complexity.
Explain how to handle noisy evaluations or flat regions.
Provide working code and a brief explanation.

Assumptions

F is convex and unimodal on [a, b].
Function evaluations may be expensive; gradients are unavailable.
Optional: evaluations may be noisy (random noise with zero mean).

Implement 1D convex minimization in Python

1D Black-Box Convex Minimization (Gradient-Free)

Task

Requirements

Assumptions

Solution (Locked)

Comments (0)